In this paper, we study the convolution structure in the special affine
Fourier transform domain to combine the advantages of the well known special
affine Fourier and Stockwell transforms into a novel integral transform coined
as special affine Stockwell transform and investigate the associated constant Q
property in the joint time frequency domain. The preliminary analysis
encompasses the derivation of the fundamental properties, Rayleighs energy
theorem, inversion formula and range theorem. Besides, we also derive a direct
relationship between the recently introduced special affine scaled Wigner
distribution and the proposed SAST. Further, we establish Heisenbergs
uncertainty principle, logarithmic uncertainty principle and Nazarovs
uncertainty principle associated with the proposed SAST. Towards the
culmination of this paper, some potential applications with simulation are
presented.Comment: arXiv admin note: text overlap with arXiv:2010.01972 by other author